137,
<i>It never goes to n over n unless you consider a adequately defined process as erasing the troubling -1.</i>
You mean, like the adequately defined limiting processes seen in the calculus of limits?
<i>I would avoid your line of reasoning myself. It is unjustifiable, either in mathematics or calculus.</i>
I've justified it in my previous post. It's justified by our observations of the world. It's justified by the axioms and derived results of mathematics.
You quoted me...
Not if relativity is correct. A test of one physical system justifies the application of the theory to the others because of what I said in the quote above.
<i>Are you saying that your FOR measurements are real and the other twin's measurements are real and that the observed measurements from each reciprocal twin's FOR are real?</i>
Yes, unless you want to go into the realism/instrumentalism philosophical argument.
<i>Some believe appearance is the reality. Some say it is merely appearances. This is not a matter of agreement.</i>
That is philosophy, not physics. They agree on the physics. All the physics needs to do is to make accurate predictions, which is what relativity does. The "meaning" of it all can be left to the philosophers.
<i>My point is that Einstein did not just happen to plug in light speed as a convenience. He made a conscious decision to use light as the speed limit of the measureable.</i>
Not exactly. The fact that light speed is a limit is a derived result, not an assumption. Einstein assumed only his two postulates.
<i>So a good clock is one that has to be affected by speed?</i>
Yes, if relativity is correct. But the mechanism of the clock is not affected. Time itself is affected, as Taylor and Wheeler point out in your quote.
<i>you state a] 2 clocks appear to run at different rates according to an observer but it is the nature of time itself. So which is it? Is it the appearance of different rates of time passage or is it actual time passage differences.</i>
Since there is no absolute reference frame, appearances are all we have to go on. We might as well call them real. So, both (a) and (b) are true. The nature of time itself varies with the observer.
<i>"Einstein says you cannot do that for light."
Please cite the source, so I can get schooled.</i>
The source was a statement by Einstein quoted by 137 in a previous post in this thread. You can easily look it up again.
<i>Well, hot damn if that don't sound like Schrodinger's cat; Open the box and you get the truth and it ruins the whole 'either-or' setup. So in transit there is an illusion, an appearance of symmetry where each one measures time dilation and length shortening of the other as a reality, when in reality only one twin's reality was slowed and shortened in an unseen reality within their own frame but viewed by the other one as an appearance which was actually a reality with the one twin who kept looking in the mirror and getting older while receiving updated photos of the other twin staying the same age. Paradox is resolved.</i>
No. In transit, each observer has his or her own reality, and the symmetry between their points of view is real. When the acceleration happens, that symmetry is broken, and <b>both</b> twins see the non-accelerating twin's time as running faster than the accelerating twin. When the accelerating twin finally slows to a stop relative to the other twin, the stay-at-home twin is agreed by both observers to be older than the one who travelled. Paradox is resolved.
<i>It never goes to n over n unless you consider a adequately defined process as erasing the troubling -1.</i>
You mean, like the adequately defined limiting processes seen in the calculus of limits?
<i>I would avoid your line of reasoning myself. It is unjustifiable, either in mathematics or calculus.</i>
I've justified it in my previous post. It's justified by our observations of the world. It's justified by the axioms and derived results of mathematics.
You quoted me...
Then you said: <i>Unacceptable limitation on testing. ... Testing is always necessary. Atomic clocks may be affected differently from light clocks from electronic clocks to mechanical clocks.</i>The argument is a general one to do with space, time and relative motion. Therefore it is generally applicable to any device or system moving in space and time.
Not if relativity is correct. A test of one physical system justifies the application of the theory to the others because of what I said in the quote above.
<i>Are you saying that your FOR measurements are real and the other twin's measurements are real and that the observed measurements from each reciprocal twin's FOR are real?</i>
Yes, unless you want to go into the realism/instrumentalism philosophical argument.
<i>Some believe appearance is the reality. Some say it is merely appearances. This is not a matter of agreement.</i>
That is philosophy, not physics. They agree on the physics. All the physics needs to do is to make accurate predictions, which is what relativity does. The "meaning" of it all can be left to the philosophers.
<i>My point is that Einstein did not just happen to plug in light speed as a convenience. He made a conscious decision to use light as the speed limit of the measureable.</i>
Not exactly. The fact that light speed is a limit is a derived result, not an assumption. Einstein assumed only his two postulates.
<i>So a good clock is one that has to be affected by speed?</i>
Yes, if relativity is correct. But the mechanism of the clock is not affected. Time itself is affected, as Taylor and Wheeler point out in your quote.
<i>you state a] 2 clocks appear to run at different rates according to an observer but it is the nature of time itself. So which is it? Is it the appearance of different rates of time passage or is it actual time passage differences.</i>
Since there is no absolute reference frame, appearances are all we have to go on. We might as well call them real. So, both (a) and (b) are true. The nature of time itself varies with the observer.
<i>"Einstein says you cannot do that for light."
Please cite the source, so I can get schooled.</i>
The source was a statement by Einstein quoted by 137 in a previous post in this thread. You can easily look it up again.
<i>Well, hot damn if that don't sound like Schrodinger's cat; Open the box and you get the truth and it ruins the whole 'either-or' setup. So in transit there is an illusion, an appearance of symmetry where each one measures time dilation and length shortening of the other as a reality, when in reality only one twin's reality was slowed and shortened in an unseen reality within their own frame but viewed by the other one as an appearance which was actually a reality with the one twin who kept looking in the mirror and getting older while receiving updated photos of the other twin staying the same age. Paradox is resolved.</i>
No. In transit, each observer has his or her own reality, and the symmetry between their points of view is real. When the acceleration happens, that symmetry is broken, and <b>both</b> twins see the non-accelerating twin's time as running faster than the accelerating twin. When the accelerating twin finally slows to a stop relative to the other twin, the stay-at-home twin is agreed by both observers to be older than the one who travelled. Paradox is resolved.